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Abstract

Achieving a greater imaging depth with two-photon fluorescence microscopy (TPFM) is mainly limited by out-of-focus fluorescence generated from both ballistic and scattered light excitation. We report on an improved signal-to-noise ratio (SNR) in a highly scattering medium as demonstrated by analytical simulation and experiments for TPFM. Our technique is based on out-of-focus rejection using a confocal pinhole. We improved the SNR by introducing the pinhole in the collection beam path. Using the radiative transfer theory and the ray-optics approach, we analyzed the effects of different sizes of pinholes on the generation of the fluorescent signal in the TPFM system. The analytical simulation was evaluated by comparing its results with the experimental results in a scattering medium. In a combined confocal pinhole and two-photon microscopy system, the imaging depth limit of approximately 5 scattering mean free paths (MFP) was found to have improved to 6.2 MFP.

Schematic diagram of TPEF collection path with pinhole. The figure only shows the on-axis terms. fo and ft are the focal length of the objective and tube lens, ro and rt are the radii of the objective and tube lens, wd is the working distance of the objective lens, ro is the objective front aperture radius, θp is the angular acceptable range according to the radius of pinhole rp, and θ is the maximum acceptance angle at each depth.

(a) A TPEF collection from an arbitrarily positioned fluorescence source. The solid angle Ω depends on the acceptable area radius ra, fluorescence distance R, and the off-axis angle γ. (b) A solid angle of the ellipse (left) and its identical solid angle of the circle (right). We assume that the areas of the ellipse and circle are identical; the solid angle is also the same (ra rγ = rm2).

Spatially distributed total collection efficiency of 20-μm pinhole (left) and non-pinhole (right) in scattering medium. The scattering coefficient at the fluorescence wavelength is 42 cm−1. Data were plotted on a semi-logarithmic scale.

Axial profiles of the collection efficiency of 20-μm (blue) and non-pinhole (red) for a focusing depth set at 2000 um. The scattering mean free path MFP at excitation and TPEF wavelength are also reported on the upper x-axis. The corresponding ratios of non-pinhole and 20 um pinhole profiles are also provided (dotted line). The scales are the same for individual collection efficiency profiles and a ratio.

Semi-logarithmic representation of excitation (black line) and TPEF collection of 20-μm pinhole (red line) and non-pinhole (blue line) pinholes for the same excitation condition as that for Fig. 1 and at μf = 42cm−1 the fluorescence wavelength of 585 nm. The corresponding ratio of the 20-μm and non-pinhole profile is also provided for comparison (dotted green line). Data were normalized by excitation intensity at the surface (z = 0).

Semi-logarithmic plot of measured and simulated axial TPEF intensity according to 20-, 50- and 150-μm-diameter pinholes (blue asterisk, red christcross, and black cross, respectively). Measured data were normalized by the surface intensity of the 20-μm pinhole and simulation data were normalized by the surface maximum value of the 20-μm pinhole. The excitation simulation was run with NA 0.5 and axial TPEF intensity was summed with 20 μm to compensate for the 20-μm thickness of the experiment.

Signal-to-noise ratio simulated with 20 μm (blue square) and non-pinhole (red circle) pinholes as a function of scattering MFP μsz. The corresponding SNR for excitation is also plotted for comparison (black triangle). The constraint of imaging depth is assumed to be fallen at SNR = 1

Averaged pulse width (black line) and each pulse width observed at each lateral r position (0, 200, 400, 600 μm) at the surface z = 0. The red line is for r = 0 μm, blue line is for r = 200 μm, pink line is for r = 400 μm, and the cyan one is for r = 600 μm from the optical axis.